Gauge approach to the symmetric teleparallel gravity

Adak, Muzaffer

doi:10.1142/s0219887818501980

Cited by 44 publications

(26 citation statements)

References 26 publications

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“…Symmetric teleparellel gravity was further developed into the f (Q) gravity theory (or coincident general relativity) in [128], and it is also known as nonmetric gravity. Various geometrical and physical aspects of symmetric teleparallel gravity have been investigated in the past two decades in a number of studies, with the interest for this theory increasing rapidly recently [129][130][131][132][133][134][135][136][137][138][139][140][141][142][143][144][145][146][147][148]. For a review of teleparallel gravity see [149].…”

Section: Introductionmentioning

confidence: 99%

f(Q, T) gravity

et al. 2019

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We propose an extension of the symmetric teleparallel gravity, in which the gravitational action L is given by an arbitrary function f of the non-metricity Q and of the trace of the matter-energy-momentum tensor T , so that L = f (Q, T). The field equations of the theory are obtained by varying the gravitational action with respect to both metric and connection. The covariant divergence of the field equations is obtained, with the geometry-matter coupling leading to the nonconservation of the energy-momentum tensor. We investigate the cosmological implications of the theory, and we obtain the cosmological evolution equations for a flat, homogeneous and isotropic geometry, which generalize the Friedmann equations of general relativity. We consider several cosmological models by imposing some simple functional forms of the function f (Q, T), corresponding to additive expressions of f (Q, T) of the form f (Q, T) = α Q + βT , f (Q, T) = α Q n+1 + βT , and f (Q, T) = −α Q −βT 2. The Hubble function, the deceleration parameter, and the matter-energy density are obtained as a function of the redshift by using analytical and numerical techniques. For all considered cases the Universe experiences an accelerating expansion, ending with a de Sitter type evolution. The theoretical predictions are also compared with the results of the standard CDM model.

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Section: Introductionmentioning

confidence: 99%

f(Q, T) gravity

et al. 2019

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“…Such gravitational theories based on nonmetricity may also be called nonmetric gravity. Different physical and geometrical properties of symmetric teleparallel gravity have been investigated in the past in a number of studies, with the interest for this type of theoretical approach to gravity rapidly increasing recently [61][62][63][64][65][66][67][68][69][70][70][71][72][73][74][75][76][77][78][79][80][81].…”

Section: Introductionmentioning

confidence: 99%

Weyl type f(Q, T) gravity, and its cosmological implications

et al. 2020

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We consider an f(Q, T) type gravity model in which the scalar non-metricity $$Q_{\alpha \mu \nu }$$Qαμν of the space-time is expressed in its standard Weyl form, and it is fully determined by a vector field $$w_{\mu }$$wμ. The field equations of the theory are obtained under the assumption of the vanishing of the total scalar curvature, a condition which is added into the gravitational action via a Lagrange multiplier. The gravitational field equations are obtained from a variational principle, and they explicitly depend on the scalar nonmetricity and on the Lagrange multiplier. The covariant divergence of the matter energy-momentum tensor is also determined, and it follows that the nonmetricity-matter coupling leads to the nonconservation of the energy and momentum. The energy and momentum balance equations are explicitly calculated, and the expressions of the energy source term and of the extra force are found. We investigate the cosmological implications of the theory, and we obtain the cosmological evolution equations for a flat, homogeneous and isotropic geometry, which generalize the Friedmann equations of standard general relativity. We consider several cosmological models by imposing some simple functional forms of the function f(Q, T), and we compare the predictions of the theory with the standard $$\Lambda $$ΛCDM model.

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“…The equivalence principle which allows eliminating locally gravitation makes it to be an integrable gauge theory. In this approach, the metric represents the gravitational field and the connection corresponds to the gauge potential [14].…”

Section: Introductionmentioning

confidence: 99%

Cosmology in symmetric teleparallel gravity and its dynamical system

2019

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We explore an extension of the symmetric teleparallel gravity denoted the f (Q) theory, by considering a function of the nonmetricity invariant Q as the gravitational Lagrangian. Some interesting properties could be found in the f (Q) theory by comparing with the f (R) and f (T ) theories. The field equations are derived in the f (Q) theory. The cosmological application is investigated. In this theory the accelerating expansion is an intrinsic property of the universe geometry without need of either exotic dark energy or extra fields. And the state equation of the geometrical dark energy can cross over the phantom divide line in the f (Q) theory. In addition, the dynamical system method are investigated. It is shown that there are five critical points in the STG model for taking f (Q) = Q + αQ 2 . The critical points P4 and P5 are stable. P4 corresponds to the geometrical dark energy dominated de Sitter universe (w ef f tot =-1), while P5 corresponds to the matter dominated universe (w ef f tot =0). Given that P4 represents an attractor, the cosmological constant problems, such as the fine tuning problem, could be solved in the STG model.

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Gauge approach to the symmetric teleparallel gravity

Cited by 44 publications

References 26 publications

f(Q, T) gravity

f(Q, T) gravity

Weyl type f(Q, T) gravity, and its cosmological implications

Cosmology in symmetric teleparallel gravity and its dynamical system

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